Muon reconstruction performance of the ATLAS detector in proton–proton collision data at √s = 13 TeV

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Article

Reference

Muon reconstruction performance of the ATLAS detector in proton–proton collision data at √s = 13 TeV

ATLAS Collaboration

ANCU, Lucian Stefan (Collab.), et al.

Abstract

This article documents the performance of the ATLAS muon identification and reconstruction using the LHC dataset recorded at s=13 TeV in 2015. Using a large sample of J/ψ→μμ and Z→μμ decays from 3.2 fb -1 of pp collision data, measurements of the reconstruction efficiency, as well as of the momentum scale and resolution, are presented and compared to Monte Carlo simulations. The reconstruction efficiency is measured to be close to 99% over most of the covered phase space ( |η|

ATLAS Collaboration, ANCU, Lucian Stefan (Collab.), et al . Muon reconstruction performance of the ATLAS detector in proton–proton collision data at √s = 13 TeV. The European Physical Journal. C, Particles and Fields , 2016, vol. 76, no. 5, p. 292

DOI : 10.1140/epjc/s10052-016-4120-y

Available at:

http://archive-ouverte.unige.ch/unige:84169

Disclaimer: layout of this document may differ from the published version.

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DOI 10.1140/epjc/s10052-016-4120-y Regular Article - Experimental Physics

Muon reconstruction performance of the ATLAS detector in proton–proton collision data at √

s=13 TeV

ATLAS Collaboration CERN, 1211 Geneva 23, Switzerland

Received: 18 March 2016 / Accepted: 29 April 2016

Abstract This article documents the performance of the ATLAS muon identification and reconstruction using the LHC dataset recorded at√

s=13 TeV in 2015. Using a large sample ofJ/ψ →μμandZ →μμdecays from 3.2 fb⁻¹ ofppcollision data, measurements of the reconstruction efficiency, as well as of the momentum scale and resolution, are presented and compared to Monte Carlo simulations. The reconstruction efficiency is measured to be close to 99 % over most of the covered phase space (|η| < 2.5 and 5< pT<100 GeV). The isolation efficiency varies between 93 and 100 % depending on the selection applied and on the momentum of the muon. Both efficiencies are well repro- duced in simulation. In the central region of the detector, the momentum resolution is measured to be 1.7 % (2.3 %) for muons from J/ψ → μμ (Z → μμ) decays, and the momentum scale is known with an uncertainty of 0.05 %.

In the region|η| >2.2, the pT resolution for muons from Z →μμdecays is 2.9 % while the precision of the momentum scale for low-pT muons from J/ψ → μμ decays is about 0.2 %.

1 Introduction

Muons are key to some of the most important physics results published by the ATLAS experiment [1] at the LHC. These results include the discovery of the Higgs boson [2] and the measurement of its properties [3–5], the precise measurement of Standard Model processes [6,7], and searches for physics beyond the Standard Model [8–11].

The performance of the ATLAS muon reconstruction during the LHC run at√

s = 7–8 TeV has been documented in recent publications [12,13]. During the 2013–2015 shutdown, the LHC was upgraded to increase the centre-of-mass energy from 8 to 13 TeV and the ATLAS detector was equipped with additional muon chambers and a new inner- most Pixel layer, the Insertable B-Layer, providing measure-

e-mail:atlas.publications@cern.ch

ments closer to the interaction point. Moreover, the muon reconstruction software was updated and improved.

After introducing the ATLAS muon reconstruction and identification algorithms, this article describes the performance of the muon reconstruction in the first dataset collected at√

s=13 TeV. Measurements of the muon reconstruction and isolation efficiencies and of the momentum scale and resolution are presented. The comparison between data and Monte Carlo (MC) simulation and the determination of the corrections to the simulation used in physics analyses are also discussed. The results are based on the analysis of a large sample of J/ψ→μμ andZ →μμdecays reconstructed in 3.2 fb⁻¹of ppcollisions recorded in 2015.

This article is structured as follows: Sect.2describes the ATLAS subdetectors that are most relevant to this work;

Sects. 3and5describe the muon reconstruction and identification in ATLAS, respectively; Sect.4describes the data samples used in the analysis; the reconstruction and isolation efficiencies are described in Sects.6and7, respectively, while the momentum scale and resolution are described in Sect.8. Finally, conclusions are given in Sect.9.

2 ATLAS detector

A detailed description of the ATLAS detector can be found in Ref. [1]. Information primarily from the inner detector (ID) and the muon spectrometer (MS), supplemented by information from the calorimeters, is used to identify and precisely reconstruct muons produced inppcollisions.

The ID consists of three subdetectors: the silicon pixels (Pixel) and the semiconductor tracker (SCT) with a pseudorapidity¹coverage up to|η| = 2.5, and the transition radi-

1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and thez-axis along the beam pipe. Thex-axis points from the IP to the centre of the LHC ring, and they-axis points upward. Cylindrical coordinates(r, φ) are used in the transverse plane,φbeing the azimuthal angle around the beam pipe. The pseudorapidity and the transverse momentum are defined in terms of the polar angleθasη= −ln tan(θ/2)and p_T=

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ation tracker (TRT) with a pseudorapidity coverage up to

|η|= 2.0. The ID measures the muon track close to the interaction point, providing accurate measurements of the track parameters inside an axial magnetic field of 2 T.

The MS is the outermost ATLAS subdetector. It is designed to detect muons in the pseudorapidity region up to|η| =2.7, and to provide momentum measurements with a relative resolution better than 3 % over a wide pT range and up to 10 % atpT≈1 TeV. The MS consists of one barrel (|η|<1.05) and two endcap sections (1.05<|η|<2.7). A system of three large superconducting air-core toroidal mag- nets, each with eight coils, provides a magnetic field with a bending integral of about 2.5 Tm in the barrel and up to 6 Tm in the endcaps. Resistive plate chambers (RPC, three dou- blet layers for|η|<1.05) and thin gap chambers (TGC, one triplet layer followed by two doublets for 1.0<|η| <2.4) provide triggering capability to the detector as well as (η,φ) position measurements with typical spatial resolution of 5–10 mm. A precise momentum measurement for muons with pseudorapidity up to|η| = 2.7 is provided by three layers of monitored drift tube chambers (MDT), with each chamber providing six to eightη measurements along the muon trajectory. For|η|>2, the inner layer is instrumented with a quadruplet of cathode strip chambers (CSC) instead of MDTs. The single-hit resolution in the bending plane for the MDT and the CSC is about 80 and 60µm, respectively.

The muon chambers are aligned with a precision between 30 and 60µm.

During the shutdown preceding the LHC Run 2, the MS was completed to its initial design [14] by adding the last missing chambers in the transition region between the barrel and the endcaps (1.0 < |η| < 1.4). Four RPC-equipped MDT chambers were also installed inside two elevator shafts to improve the acceptance in that region compared to Run 1.

Some of the new MDT chambers are made of tubes with a smaller radius compared to the ones used in the rest of the detector, allowing the detector to cope with higher rates.

The material between the interaction point (IP) and the MS ranges approximately from 100 to 190 radiation lengths, depending onη, and consists mostly of calorimeters.

The lead/liquid-argon electromagnetic calorimeter covers

|η| < 3.2. It is surrounded by hadronic calorimeters made of steel and scintillator tiles for|η| < 1.7, and copper or tungsten and liquid argon for|η|>1.7.

3 Muon reconstruction

Muon reconstruction is first performed independently in the ID and MS. The information from individual subdetectors is then combined to form the muon tracks that are used in psinθ, respectively. Theη–φdistance between two particles is defined asR=

(η)²+(φ)².

physics analyses. In the ID, muons are reconstructed like any other charged particles as described in Refs. [15,16].

This section focuses on the description of the muon reconstruction in the MS (Sect.3.1) and on the combined muon reconstruction (Sect.3.2).

3.1 Muon reconstruction in the MS

Muon reconstruction in the MS starts with a search for hit patterns inside each muon chamber to form segments. In each MDT chamber and nearby trigger chamber, a Hough transform [17] is used to search for hits aligned on a trajectory in the bending plane of the detector. The MDT segments are reconstructed by performing a straight-line fit to the hits found in each layer. The RPC or TGC hits measure the coordinate orthogonal to the bending plane. Segments in the CSC detectors are built using a separate combinatorial search in theηandφdetector planes. The search algorithm includes a loose requirement on the compatibility of the track with the luminous region.

Muon track candidates are then built by fitting together hits from segments in different layers. The algorithm used for this task performs a segment-seeded combinatorial search that starts by using as seeds the segments generated in the middle layers of the detector where more trigger hits are available.

The search is then extended to use the segments from the outer and inner layers as seeds. The segments are selected using criteria based on hit multiplicity and fit quality and are matched using their relative positions and angles. At least two matching segments are required to build a track, except in the barrel–endcap transition region where a single high- quality segment with ηand φ information can be used to build a track.

The same segment can initially be used to build several track candidates. Later, an overlap removal algorithm selects the best assignment to a single track, or allows for the segment to be shared between two tracks. To ensure high efficiency for close-by muons, all tracks with segments in three different layers of the spectrometer are kept when they are identical in two out of three layers but share no hits in the outermost layer.

The hits associated with each track candidate are fitted using a global χ² fit. A track candidate is accepted if the χ² of the fit satisfies the selection criteria. Hits providing large contributions to theχ²are removed and the track fit is repeated. A hit recovery procedure is also performed looking for additional hits consistent with the candidate trajectory.

The track candidate is refit if additional hits are found.

3.2 Combined reconstruction

The combined ID–MS muon reconstruction is performed according to various algorithms based on the information

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provided by the ID, MS, and calorimeters. Four muontypes are defined depending on which subdetectors are used in reconstruction:

• Combined (CB) muon: track reconstruction is performed independently in the ID and MS, and a combined track is formed with a global refit that uses the hits from both the ID and MS subdetectors. During the global fit procedure, MS hits may be added to or removed from the track to improve the fit quality. Most muons are reconstructed following an outside-in pattern recognition, in which the muons are first reconstructed in the MS and then extrapolated inward and matched to an ID track. An inside-out combined reconstruction, in which ID tracks are extrapolated outward and matched to MS tracks, is used as a complementary approach.

• Segment-tagged (ST) muons: a track in the ID is classified as a muon if, once extrapolated to the MS, it is associated with at least one local track segment in the MDT or CSC chambers. ST muons are used when muons cross only one layer of MS chambers, either because of their low pTor because they fall in regions with reduced MS acceptance.

• Calorimeter-tagged (CT) muons: a track in the ID is identified as a muon if it can be matched to an energy deposit in the calorimeter compatible with a minimum-ionizing particle. This type has the lowest purity of all the muon types but it recovers acceptance in the region where the ATLAS muon spectrometer is only partially instrumented to allow for cabling and services to the calorimeters and inner detector. The identification criteria for CT muons are optimised for that region (|η|<0.1) and a momentum range of 15< pT<100 GeV.

• Extrapolated (ME) muons: the muon trajectory is reconstructed based only on the MS track and a loose requirement on compatibility with originating from the IP. The parameters of the muon track are defined at the interaction point, taking into account the estimated energy loss of the muon in the calorimeters. In general, the muon is required to traverse at least two layers of MS chambers to provide a track measurement, but three layers are required in the forward region. ME muons are mainly used to extend the acceptance for muon reconstruction into the region 2.5<|η|<2.7, which is not covered by the ID.

Overlaps between different muon types are resolved before producing the collection of muons used in physics analyses. When two muon types share the same ID track, preference is given to CB muons, then to ST, and finally to CT muons. The overlap with ME muons in the muon system is resolved by analyzing the track hit content and selecting the track with better fit quality and larger number of hits.

The muon reconstruction used in this work evolved from the algorithms defined asChain 3in Ref. [12]. These algorithms were improved in several ways. The use of a Hough transform to identify the hit patterns for seeding the segment- finding algorithm makes the reconstruction faster and more robust against misidentification of hadrons, thus providing better background rejection early in the pattern recognition process. The calculation of the energy loss in the calorimeter was also improved. An analytic parameterization of the average energy loss is derived from a detailed description of the detector geometry. The final estimate of the energy loss is obtained by combining the analytic parameterization with the energy measured in the calorimeter. This method yields a precision on the mean energy loss of about 30 MeV for 50 GeV muons.

4 Data and Monte Carlo samples

The efficiency measurements presented in this article are obtained from the analysis of 3.2 fb⁻¹of ppcollision data recorded at √

s = 13 TeV at the LHC in 2015 during the data-taking period with 25 ns spacing between bunch cross- ings. About 1.5 M Z →μμand 3.5 M J/ψ→μμevents are reconstructed and used for the analysis. For the study of the momentum calibration, 2.7 fb⁻¹of data were used, rejecting the runs in which the longitudinal position of the beam spot was displaced by about 3 cm with respect to the centre of the detector.

Events are accepted only if the ID, the MS, and the calorimeters were operational and the solenoid and toroid magnet systems were both active. The online event selection was performed by a two-level trigger system derived from the one described in Ref. [18]. TheZ →μμcandidates are triggered by the presence of at least one muon candidate with a transverse momentum,pT, of at least 20 GeV. For the reconstruction efficiency and momentum calibration studies, the muon firing the trigger is required to be isolated (see Sect.7).

TheJ/ψ→μμcandidates used for the momentum calibration are triggered by a dedicated dimuon trigger that requires two opposite-charge muons, each withpT>4 GeV, compatible with the same vertex, and with a dimuon invariant mass in the range 2.5–4.5 GeV. TheJ/ψ→μμsample used for the efficiency measurement is selected using a combination of single-muon triggers and triggers requiring one muon with transverse momentum of at least 4 GeV and an ID track such that the invariant mass of the muon+track pair, under a muon mass hypothesis, is compatible with the mass of the J/ψ.

Monte Carlo samples for the process

pp → (Z/γ^∗)X → μμX are generated using the POWHEG BOX [19] interfaced to PYTHIA8 [20] and the CT10 [21] parton distribution functions. The PHOTOS [22]

package is used to simulate final-state photon radiation inZ

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boson decays. Samples of prompt J/ψ→μμ decays are generated using PYTHIA8 complemented with PHOTOS to simulate the effects of final-state radiation. A requirement on the minimum transverse momentum of each muon (pT > 4 GeV) is applied at the generator level. The samples used for the simulation of the backgrounds toZ →μμ include: Z → ττ, W → μν, and W → τν, gener- ated with POWHEG BOX;W W, Z Z, andW Z generated with SHERPA [23]; tt¯samples generated with POWHEG BOX+PYTHIA8; andbb¯andc¯csamples generated with PYTHIA8.

All the generated samples are passed through the simulation of the ATLAS detector based on GEANT4 [24,25] and are reconstructed with the same programs used for the data.

The ID and the MS are simulated with an ideal geometry assuming no misalignment.

The effect of multipleppinteractions per bunch crossing (“pile-up”) is modelled by overlaying simulated minimum- bias events onto the original hard-scattering event. Monte Carlo events are then reweighted so that the distribution of the average number of interactions per event agrees with the data.

5 Muon identification

Muon identification is performed by applying quality requirements that suppress background, mainly from pion and kaon decays, while selecting prompt muons with high efficiency and/or guaranteeing a robust momentum measurement.

Muon candidates originating from in-flight decays of charged hadrons in the ID are often characterized by the presence of a distinctive “kink” topology in the reconstructed track. As a consequence, it is expected that the fit quality of the resulting combined track will be poor and that the momentum measured in the ID and MS may not be compatible. Several variables offering good discrimination between prompt muons and background muon candidates are studied in simulatedtt¯events. Muons fromWdecays are categorized assignalmuons while muon candidates from light-hadron decays are categorized asbackground. For CB tracks, the variables used in muon identification are:

• q/p significance, defined as the absolute value of the dif- ference between the ratio of the charge and momentum of the muons measured in the ID and MS divided by the sum in quadrature of the corresponding uncertainties;

• ρ, defined as the absolute value of the difference between the transverse momentum measurements in the ID and MS divided by the pTof the combined track;

• normalisedχ²of the combined track fit.

To guarantee a robust momentum measurement, specific requirements on the number of hits in the ID and MS are used. For the ID, the quality cuts require at least one Pixel hit, at least five SCT hits, fewer than three Pixel or SCT holes, and that at least 10 % of the TRT hits originally assigned to the track are included in the final fit; the last requirement is only employed for|η|between 0.1 and 1.9, in the region of full TRT acceptance. A hole is defined as an active sensor traversed by the track but containing no hits. A missing hit is considered a hole only when it falls between hits successfully assigned to a given track. If some inefficiency is expected for a given sensor, the requirements on the number of Pixel and SCT hits are reduced accordingly.

Four muon identification selections (Medium, Loose, Tight, andHigh-pT) are provided to address the specific needs of different physics analyses.Loose,Medium, andTightare inclusive categories in that muons identified with tighter requirements are also included in the looser categories.

MediummuonsTheMediumidentification criteria provide the default selection for muons in ATLAS. This selection minimises the systematic uncertainties associated with muon reconstruction and calibration. Only CB and ME tracks are used. The former are required to have≥3 hits in at least two MDT layers, except for tracks in the|η|<0.1 region, where tracks with at least one MDT layer but no more than one MDT hole layer are allowed. The latter are required to have at least three MDT/CSC layers, and are employed only in the 2.5 < |η| < 2.7 region to extend the acceptance outside the ID geometrical coverage. A loose selection on the compatibility between ID and MS momentum measurements is applied to suppress the contamination due to hadrons misidentified as muons. Specifically, theq/p significanceis required to be less than seven. In the pseudorapidity region

|η| <2.5, about 0.5 % of the muons classified asMedium originate from the inside-out combined reconstruction strat- egy.

LoosemuonsTheLooseidentification criteria are designed to maximise the reconstruction efficiency while providing good-quality muon tracks. They are specifically optimised for reconstructing Higgs boson candidates in the four-lepton final state [5]. All muon types are used. All CB and ME muons satisfying theMediumrequirements are included in theLooseselection. CT and ST muons are restricted to the

|η|<0.1 region. In the region|η|<2.5, about 97.5 % of the Loosemuons are combined muons, approximately 1.5 % are CT, and the remaining 1 % are reconstructed as ST muons.

TightmuonsTightmuons are selected to maximise the purity of muons at the cost of some efficiency. Only CB muons with hits in at least two stations of the MS and satisfying the Medium selection criteria are considered. The normalised χ²of the combined track fit is required to be<8 to remove pathological tracks. A two-dimensional cut in theρandq/p significancevariables is performed as a function of the muon

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Table 1 Efficiency for prompt muons fromW decays and hadrons decaying in-flight and misidentified as prompt muons computed using att¯MC sample. The results are shown for the four identification selection criteria separating low (4 < p_T < 20 GeV) and high (20 < p_T < 100 GeV) momentum muons for candidates with

|η|<2.5. The statistical uncertainties are negligible

Selection 4<p_T<20 GeV 20<p_T<100 GeV ^MC_μ [%] Hadrons^MC [%] ^MC_μ [%] Hadrons^MC [%]

Loose 96.7 0.53 98.1 0.76

Medium 95.5 0.38 96.1 0.17

Tight 89.9 0.19 91.8 0.11

High-pT 78.1 0.26 80.4 0.13

pT to ensure stronger background rejection for momenta below 20 GeV where the misidentification probability is higher.

High-pT muons TheHigh-pT selection aims to maximise the momentum resolution for tracks with transverse momentum above 100 GeV. The selection is optimised for searches for high-massZandWresonances [8,9]. CB muons pass- ing theMediumselection and having at least three hits in three MS stations are selected. Specific regions of the MS where the alignment is suboptimal are vetoed as a precaution.

Requiring three MS stations, while reducing the reconstruction efficiency by about 20 %, improves thepTresolution of muons above 1.5 TeV by approximately 30 %.

The reconstruction efficiencies forsignalandbackground obtained fromt t simulation are reported in Table 1. The results are shown for the four identification selection criteria separating low (4 < pT < 20 GeV) and high (20 < pT < 100 GeV) transverse momentum muon candidates. No isolation requirement is applied in the selection shown in the table. When isolation requirements are applied, the misidentification rates are reduced by more than an order of magnitude. It should be noted that the higher misidentification rate observed forLoosewith respect toMediummuons is mainly due to CT muons in the region|η|<0.1.

The misidentification probability estimated with the MC simulation is validated in data by measuring the probability that pions are reconstructed as muons. An unbiased sample of pions from K_S⁰ → π⁺π⁻ decays is collected with calorimeter-based (photon, electron, jet) triggers. Good agreement between data and simulation is observed independent of thepT,η, and impact parameter of the track.

6 Reconstruction efficiency

As the muon reconstruction in the ID and MS detectors is performed independently, a precise determination of the muon reconstruction efficiency in the region|η|<2.5 is obtained with the tag-and-probe method, as described in the Sect.6.1.

A different methodology, described in Sect.6.2, is used in the region 2.5 <|η| <2.7 where muons are reconstructed using only the MS detector.

6.1 Efficiency measurement in the region|η|<2.5 The tag-and-probe method is employed to measure the efficiency of the muon identification selections within the acceptance of the ID (|η| < 2.5). The method is based on the selection of an almost pure muon sample fromJ/ψ→μμ or Z →μμevents, requiring one leg of the decay (tag) to be identified as aMediummuon that fires the trigger and the second leg (probe) to be reconstructed by a system independent of the one being studied. A selection based on the event topology is used to reduce the background contamination.

Three kinds of probes are used to measure muon efficiencies. ID tracks and CT muons both allow a measurement of the efficiency in the MS, while MS tracks are used to determine the complementary efficiency of the muon reconstruction in the ID. Compared to ID tracks, CT muons offer a more powerful rejection of backgrounds, especially at low transverse momenta, and are therefore the preferred probe type for this part of the measurement. ID tracks are used as a cross-check and for measurements not directly accessible to CT muons. A direct measurement of the CT muon reconstruction efficiency is possible using MS tracks.

The efficiency measurement for Medium, Tight, and High-pTmuons consists of two stages. First, the efficiency (X|CT) (X = Medium/Tight/High-pT) of reconstructing these muons assuming a reconstructed ID track is measured using a CT muon as probe. Then, this result is corrected by the efficiency (ID|MS)of the ID track reconstruction, measured using MS probes:

(X)= (X|ID)· (ID)= (X|CT)· (ID|MS)

(X=Medium/Tight/High-p_T). (1) A similar approach is used when using ID probe tracks for cross-checks.

This approach is valid if two assumptions are satisfied:

• the ID track reconstruction efficiency is independent from the muon spectrometer track reconstruction ( (ID) = (ID|MS)).

• the use of a CT muon as a probe instead of an ID track does not affect the probability forMedium,Tight, orHigh-pT

reconstruction ( (X|ID)= (X|CT)).

Both assumptions have been tested using generator-level information from simulation and small differences are taken into account in the systematic uncertainties.

The muons selected by theLooseidentification requirements are decomposed into two samples: CT muons within

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|η| < 0.1 and all other muons. The CT muon efficiency is measured using MS probe tracks, while the efficiency of other muons is evaluated using CT probe muons in a fashion similar to theMedium,Tight, andHigh-pTcategories.

The level of agreement of the measured efficiency, ^Data(X), with the efficiency measured with the same method in simulation,^MC(X), is expressed as the ratio of these two numbers, called the “efficiency scale factor” (SF):

SF= ^Data(X)

^MC(X). (2)

This quantity describes the deviation of the simulation from the real detector behaviour, and is of particular interest to physics analyses, where it is used to correct the simulation.

6.1.1 The tag-and-probe method with Z→μμevents Events are selected by requiring muon pairs with an invariant mass within 10 GeV of the Z boson mass. The tag muon is required to satisfy theLooseisolation (see Sect.7.2) andMedium muon identification selections and to have a transverse momentum of at least 24 GeV. Requirements on the significance of the transverse impact parameter d0

(|d0|/σ(d0) <3.0) and on the longitudinal impact parameter|z0|(|z0|<10 mm) of the tag muon are imposed. Finally, the tag muon is required to have triggered the readout of the event.

The probe muon is required to have a transverse momentum of at least 10 GeV and to satisfy theLooseisolation criteria. While this is sufficient to ensure high purity in the case of MS probe tracks, further requirements are applied to both the ID track and CT muon probes. In the case of ID tracks, an isolation requirement is applied which is consid- erably stricter than theLooseselection in order to suppress backgrounds as much as possible. In addition, the invariant mass window is tightened to 5 GeV around the Z boson mass, rather than the 10 GeV used in the other cases. For CT muon probes, additional requirements on the compatibility of the associated calorimeter energy deposit with a muon signature are applied to further enhance the purity. The ID probe tracks and calorimeter-tagged probe muons must also have transverse and longitudinal impact parameters consistent with being produced in a primary pp interaction, as required for tag muons. A probe is considered successfully reconstructed if a reconstructed muon is found within a cone in theη–φplane of sizeR=0.05 around the probe track.

A small fraction (about 0.1 %) of the selected tag–probe pairs originates from sources other thanZ →μμevents. For a precise efficiency measurement, these backgrounds must be estimated and subtracted. Contributions from Z → ττ andtt¯decays are estimated using simulation. Additionally, multijet events and W → μν decays in association with

jet activity (W+jets) can yield tag–probe pairs through sec- ondary muons from heavy- or light-hadron decays. As these backgrounds are approximately charge-symmetric, they are estimated from the data using same-charge (SC) tag–probe pairs. This leads to the following estimate of the opposite- charge (OC) background,N^Bkg, for each region of the kinematic phase-space:

N^Bkg=N_OC^Z^,^t^¯^t^MC+T ·

N_SC^Data−N_SC^Z^,^t^t^¯^MC

(3) where N_OC^Z^,^t^t^¯^MC is the contribution from Z → ττ andtt¯ decays, N_SC^Data is the number of SC pairs measured in data andN_SC^Z^,^t^t^¯^MCis the estimated contribution of theZ →μμ, Z → ττ, andtt¯processes to the SC sample.T is a global transfer factor that takes into account the charge asymmetry of the multijet andW+jets processes, estimated in data using a control sample of events obtained by inverting the probe isolation requirement. For MS (ID) tracks, a value ofT =1.7 (1.1)is obtained, while for calorimeter-tagged muon probes the transfer factor isT =1.2. The systematic uncertainties in the transfer factor vary between 40 % and 100 % and are included in the systematic error in the reconstruction efficiency described in Sect.6.1.3.

The efficiency measured in the data is corrected for the background contributions described above by subtracting the predicted probe yields attributed to these sources from the number of observed probes,

= N_R^Data−N_R^Bkg

N_P^Data−N_P^Bkg, (4)

where NP denotes the total number of probes and NR the number of successfully reconstructed probes. The resulting efficiency can then be compared directly to the result of the simulation.

6.1.2 The tag-and-probe method with J/ψ→μμevents The reconstruction efficiencies of theLoose,Medium, and Tightmuon selections at low pTare measured from a sample of J/ψ→μμ events selected using a combination of single-muon triggers and the dedicated “muon + track” trigger described in Sect.4.

Tag–probe pairs are selected within the invariant mass window of 2.7–3.5 GeV and requiring a transverse momentum of at least 5 GeV for each muon. The tag muon is required to satisfy theMediummuon identification selection and to have triggered the readout of the event. In order to avoid low- momentum curved tracks sharing the same trigger region, tag and probe muons are required to be R > 0.2 apart when extrapolated to the MS trigger surfaces. Finally, they

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η

−2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5

Relative Uncertainty [%]

−3

10

−2

10

−1

10 1 10 102

103

Truth Closure Background Statistics Statistics (MC) Total

ATLAS = 13 TeV, 3.2 fb-1 s

muons Medium

μ μ

→ Z

η

−2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5

−3

10

−2

10

−1

10 1 10 102

103

Truth closure Statistics (MC) Background Statistics

Signal Total

ATLAS = 13 TeV, 3.2 fb-1 s

muons Medium

μ μ

→ ψ J/

Fig. 1 Total uncertainty in the efficiency scale factor forMediummuons as a function ofηas obtained fromZ→μμdata (left) for muons with p_T>10 GeV, and fromJ/ψ→μμdata (right) for muons with 5< p_T<20 GeV. The combined uncertainty is the sum in quadrature of the individual contributions

are selected withz0 ≡ |z^tag₀ −z^probe₀ | < 5 mm, to suppress background. A probe is considered successfully reconstructed if a selected muon is found within aR = 0.05 cone around the probe track.

The background contamination and the muon reconstruction efficiency are measured with a simultaneous maximum- likelihood fit of two statistically independent distributions of the invariant mass: events in which the probe is or is not successfully matched to the selected muon. The fits are performed in six pT and nineηbins of the probe tracks. The signal is modelled with a Crystal Ball function [26] with a single set of parameters for the two independent samples.

Separate first-order polynomial fits are used to describe the background shape for matched and unmatched probes.

6.1.3 Systematic uncertainties

The main contributions to the systematic uncertainty in the measurement of the efficiency SFs with Z →μμ and J/ψ→μμevents are shown in Figs.1and2, as a function ofηandpT, respectively.

The uncertainty in the background estimate is evaluated in theZ →μμanalysis by taking the maximum variation of the transfer factorTwhen estimated with a simulation-based approach as described in Ref. [12] and when assuming the background to be charge-symmetric. This results in an uncertainty of the efficiency measurement below 0.1 % over a large momentum range, but reaching∼1 % for low muon momenta where the contribution of the background is most significant.

In the J/ψ→μμ analysis, the background uncertainty is estimated by changing the function used in the fit to model the background, replacing the first-order polynomial with an exponential function. An uncertainty due to the signal mod- elling in the fit, labelled as “Signal” in Figs.1and2, is also estimated using a convolution of exponential and Gaussian

[GeV]

pT

6 7 8 910 20 30 40 50 60 10²

−2

10

−1

10 1 10 102

103

Truth closure Background Signal Statistics (MC) Statistics Total

Truth closure Background Statistics (MC) Statistics Total ATLAS

= 13 TeV, 3.2 fb-1

s

muons Medium μ

μ

→ ψ

J/ Z→μμ

Fig. 2 Total uncertainty in the efficiency scale factor for Medium muons as a function of p_T as obtained from Z→μμ(solid lines) and J/ψ→μμ(dashed lines) decays. The combined uncertainty is the sum in quadrature of the individual contributions

functions as an alternative model. Each uncertainty is about 0.1 %.

The cone size used for matching selected muons to probe tracks is optimised in terms of efficiency and purity of the matching. The systematic uncertainty deriving from this choice is evaluated by varying the cone size by±50 %. This yields an uncertainty below 0.1 % in both analyses.

Possible biases in the tag-and-probe method, such as biases due to different kinematic distributions between reconstructed probes and generated muons or correlations between ID and MS efficiencies, are estimated in simulation by comparing the efficiency measured with the tag-and-probe method with the “true” efficiency given by the fraction of generator-level muons that are successfully reconstructed.

This uncertainty is labelled as “Truth Closure” in Figs. 1 and2. In theZ →μμanalysis, agreement better than 0.1 % is observed in the high momentum range. This uncertainty

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Efficiency 0.96 0.98 1

0.6 0.65 ^ATLAS

= 13 TeV, 3.2 fb-1

s Data

MC μ μ

→ Z

2.5 η

− −2−1.5−1−0.5 0 0.5 1 1.5 2 2.5

Data / MC^0.98

1

1.02 ^{Stat only} ^Sys^⊕^Stat

muons Medium

| < 0.1) η muons (|

Loose

Efficiency

0.85 0.9 0.95 1

0.45 0.5 0.55 0.6

ATLAS = 13 TeV, 3.2 fb-1 s

muons Tight

Data MC μ μ

→ Z

η

−2.5−2−1.5−1−0.5 0 0.5 1 1.5 2 2.5

Data / MC

0.95 1

Efficiency

0.5 1

ATLAS = 13 TeV, 3.2 fb-1

s muons High-pT

μ μ

→ Z

Data MC

η

−2.5−2−1.5−1−0.5 0 0.5 1 1.5 2 2.5

Data / MC

0.9 1

Fig. 3 Muon reconstruction efficiency as a function ofηmeasured in Z→μμevents for muons with p_T > 10 GeV shown forMedium (top),Tight(bottom left), andHigh-p_T(bottom right) muon selections.

In addition, the top plot also shows the efficiency of theLooseselec- tion (squares) in the region|η|< 0.1 where theLooseandMedium

selections differ significantly. Theerror barson the efficiencies indi- cate the statistical uncertainty.Panels at the bottomshow the ratio of the measured to predicted efficiencies, with statistical and systematic uncertainties

grows at lowpT, and differences up to 0.7 % are found in the J/ψ→μμanalysis. A larger effect of up to 1–2 % is measured in both analyses in the region|η|<0.1. In the extrac- tion of the efficiency scale factors, the difference between the measured and the “true” efficiency cancels to first order.

To take into account possible imperfections of the simulation, half of the observed difference is used as an additional systematic uncertainty in the SF.

No significant dependence of the measured SFs with pT is observed in the momentum range considered in the Z →μμ analysis. An upper limit on the SF variation for large muon momenta is extracted from simulation, leading to an additional uncertainty of 2–3 % per TeV for muons with pT>200 GeV. The efficiency scale factor is observed to be independent of the amount of pile-up.

6.1.4 Results

Figure3shows the muon reconstruction efficiency as a function ofηas measured fromZ →μμevents for the different

muon selections. The efficiency as measured in data and the corresponding scale factors for theMediumselection are also shown in Fig.4as a function ofηandφ. The efficiency at low pTis reported in Fig.5as measured from J/ψ→μμ events as a function of pTin differentηregions.

The efficiencies of theLooseandMediumselections are very similar throughout the detector with the exception of the region|η|<0.1, where theLooseselection fills the MS acceptance gap using the calorimeter and segment-tagged muons contributions. The efficiency of these selections is observed to be in excess of 98 %, and between 90 and 98 % for theTightselection, with all efficiencies in very good agreement with those predicted by the simulation. An inefficiency due to a poorly aligned MDT chamber is clearly localised at(η, φ)∼ (−1.3,1.6), and is the most significant feature of the comparison between collision data and simulation for these three categories. In addition, a 2 %-level local inefficiency is visible in the region(η, φ)∼(1.9,2.5), traced to temporary failures in the SCT readout system. Further local inefficiencies in the barrel region aroundφ∼ −1.1 are also

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Fig. 4 Reconstruction efficiency measured in data (top), and the data/MC efficiency scale factor (bottom) forMediummuons as a function ofηandφfor muons with p_T>10 GeV inZ→μμ events. Thethin white bins visible in the region|φ| ∼πare due to the different bin boundaries inφin the endcap and barrel regions

η

−2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5

φ

−3

−2

−1 0

1 2 3

Data Efficiency [%]

0 20 40 60 80 100

97.7 98.8 97.9 98.7 98.6 98.5 98.4 98.9 98.3

98.9 98.7 99.0 98.1 98.5 99.0 98.4

98.9 99.4 98.8 99.3 99.4 99.5 98.5 99.3 99.4

99.6 99.0 99.5 99.4 99.5 99.5 99.4

99.0 98.9 99.0 99.3 98.9 99.2 98.5 99.2 99.4

99.1 99.0 99.2 99.3 99.2 99.4 99.3

99.5 99.5 99.7 99.4 100.0 99.4 99.2 99.7 99.7

99.2 99.9 99.6 99.7 99.4 99.8 99.6

99.4 99.5 99.6 99.1 97.5 99.2 99.4 99.5 98.9

99.5 99.3 99.3 99.5 99.1 99.4 99.4

98.9 99.2 98.3 95.8 82.1 98.8 99.4 99.4 99.2

98.9 98.4 98.9 99.3 98.9 98.2 99.2

99.4 98.5 98.6 98.3 99.4 98.9 99.5 98.6 99.7

98.6 99.0 98.6 99.4 98.6 99.6 98.8

99.3 99.2 98.5 99.2 99.4 99.4 99.6 99.3 99.5

99.2 99.0 97.5 98.7 94.0 99.4 99.2

99.3 99.0 98.6 98.2 99.6 99.2 99.6 99.2 99.4

99.0 98.8 99.1 99.5 98.8 99.5 99.2

99.5 99.0 98.6 99.0 99.5 99.3 98.1 99.4 99.4

99.3 98.9 97.7 99.3 97.8 99.5 99.4

55.2 91.2 60.8 90.3 44.9 86.1 2.7 81.9 7.9

84.4 17.0 86.4 61.8 86.8 16.2 87.9

99.6 99.3 98.6 99.2 99.5 99.1 97.4 99.1 98.3

99.3 98.4 97.7 99.3 97.6 99.5 99.3

99.7 98.9 99.4 99.3 99.7 99.2 99.7 99.1 99.5

99.2 98.4 98.9 99.5 98.6 99.4 99.5

99.5 99.0 99.1 99.3 99.6 99.1 99.5 99.4 99.4

99.4 98.5 98.2 99.5 87.4 99.5 99.2

99.7 98.2 99.4 98.4 99.5 98.5 99.5 98.7 99.5

99.0 99.0 98.5 99.4 98.5 99.4 98.5

99.1 99.3 99.5 99.5 99.4 99.1 99.8 99.4 99.6

99.3 98.5 98.7 99.8 98.8 98.6 99.1

99.5 99.6 99.6 98.9 98.6 99.2 99.4 99.4 99.3

99.6 99.5 99.0 99.7 99.0 99.2 99.3

99.6 99.6 99.5 99.5 99.7 99.6 99.7 100.0 99.4

99.5 99.6 99.4 99.5 99.7 99.7 99.5

99.3 99.3 99.4 99.3 98.9 99.1 97.7 98.1 98.9

99.1 99.2 99.2 99.3 99.2 99.0 99.5

99.5 99.7 99.5 99.6 99.7 99.6 99.2 99.2 98.5

99.4 99.5 99.6 99.5 99.5 99.5 99.6

98.2 98.7 98.5 98.8 98.1 98.7 98.6 98.8 98.6

98.8 99.1 98.9 98.8 99.0 98.3 99.1

ATLAS

= 13 TeV, 3.2 fb-1

s

muons Medium

η

−2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5

φ

−3

−2

−1 0

1 2 3

Data/MC [%]

60 70 80 90 100 110

98.0 99.0 98.3 99.0 98.9 98.9 98.8 99.4 98.7

99.2 99.1 99.3 98.4 98.8 99.4 98.7

99.1 99.6 99.1 99.5 99.7 99.7 98.6 99.5 99.5

99.8 99.4 99.7 99.6 99.7 99.7 99.6

99.4 99.3 99.5 99.8 99.3 99.7 98.9 99.6 99.8

99.5 99.5 99.6 99.6 99.6 99.9 99.7

99.7 99.8 99.9 99.7 100.3 99.7 99.5 100.0 99.9

99.5 100.2 99.9 99.8 99.6 100.0 99.8

99.9 100.0 99.9 99.7 98.2 99.8 99.7 99.9 99.3

99.9 99.7 100.0 99.8 99.7 99.8 99.9

99.6 99.8 99.0 96.5 82.6 99.6 100.1 100.0 99.8

99.6 99.2 99.6 99.9 99.6 99.1 99.8

99.8 99.4 99.0 99.4 99.8 99.8 99.8 99.6 100.0

99.5 99.3 99.1 99.8 99.0 100.0 99.8

99.6 99.7 98.9 99.6 99.7 99.8 100.0 99.7 99.8

99.6 99.3 98.3 99.1 94.9 99.8 99.6

99.5 99.4 98.9 98.6 99.9 99.6 99.9 99.7 99.7

99.5 99.2 99.7 99.8 99.3 99.8 99.6

100.0 99.3 99.1 99.3 99.8 99.7 100.2 99.8 99.7

99.6 99.3 99.7 99.6 99.7 99.9 99.7

99.6 99.3 98.7 99.7 101.1 99.3 90.6 99.5 100.1

98.8 105.3 99.1 100.6 100.0 103.4 99.3

99.8 99.7 99.0 99.6 99.8 99.6 99.3 99.6 100.1

99.6 98.7 99.6 99.6 99.4 99.8 99.7

100.0 99.3 99.8 99.8 100.0 99.6 99.9 99.6 99.8

99.6 98.8 99.5 99.8 99.1 99.8 99.9

99.8 99.4 99.5 99.7 99.8 99.5 99.7 99.8 99.8

99.8 98.8 99.0 99.8 88.1 100.0 99.6

100.0 99.2 99.7 99.4 99.7 99.5 99.8 99.9 99.9

99.9 99.4 98.9 99.8 98.9 99.8 99.6

99.9 100.2 100.0 100.5 99.9 100.1 100.6 100.3 100.2

100.1 99.4 99.5 100.3 99.7 99.5 100.0

99.9 100.1 100.0 99.5 99.4 99.8 99.9 99.9 99.7

100.0 99.9 99.6 100.1 99.7 99.7 99.8

99.8 99.9 99.8 99.8 100.0 99.9 100.0 100.2 99.7

99.7 99.9 99.7 99.8 99.9 99.9 99.8

99.7 99.7 99.8 99.8 99.3 99.5 98.1 98.5 99.3

99.5 99.6 99.6 99.7 99.7 99.5 99.8

99.6 99.8 99.8 99.8 99.9 99.8 99.4 99.4 98.6

99.6 99.8 99.8 99.8 99.7 99.6 99.8

98.6 99.0 99.0 99.3 98.5 99.0 98.9 99.1 98.9

99.1 99.6 99.2 99.1 99.3 98.6 99.4

ATLAS

= 13 TeV, 3.2 fb-1

s

muons Medium

Efficiency

0.7 0.8 0.9 1

ATLAS = 13 TeV, 3.2 fb-1

s muons Loose

Data MC

μ μ

→ ψ J/

Data / MC

0.95 1 1.05

<-2.0 η -2.5<

<-1.5 η -2.0<

<-1.05 η -1.5<

<-0.1 η -1.05<

<0.1 η -0.1<

<1.05 η 0.1<

<1.5 η 1.05<

<2.0 η

1.5< η<2.5

2.0<

(5-15) GeV

pT Stat only Sys⊕ Stat

Efficiency

0.6 0.8 1

ATLAS = 13 TeV, 3.2 fb-1

s muons Tight

Data MC

μ μ

→ ψ J/

Data / MC 0.9

1 1.1

<-2.0 η -2.5<

<-1.5 η -2.0<

<-1.05 η -1.5<

<-0.1 η -1.05<

<0.1 η

-0.1< η<1.05

0.1<

<1.5 η 1.05<

<2.0 η 1.5<

<2.5 η 2.0<

(5-15) GeV

pT Stat only Sys⊕ Stat

Fig. 5 Muon reconstruction efficiency in differentηregions measured inJ/ψ→μμevents forLoose(left) andTight(right) muon selections.

Within eachηregion, the efficiency is measured in six p_Tbins (5–6, 6–7, 7–8, 8–10, 10–12, and 12–15 GeV). The resulting values are plot- ted as distinct measurements in eachηbin withp_Tincreasing from 5 to

15 GeV going fromlefttoright. Theerror barson the efficiencies indi- cate the statistical uncertainty. Thepanel at the bottomshows the ratio of the measured to predicted efficiencies, with statistical and systematic uncertainties

linked to temporary faults during data taking. The efficiency of theHigh-pT selection is significantly lower, as a consequence of the strict requirements on momentum resolution.

Local disagreements between prediction and observation are more severe than in the case of the other muon selections.

Apart from the poorly aligned MDT chamber, they are most prominent in the CSC region.

Figure 6 shows the reconstruction efficiencies for the Mediummuon selection as a function of transverse momentum, including results from Z →μμ andJ/ψ→μμ, for